When I took discrete math as an adult I realized that this was a subject I would have enjoyed and done well at much earlier in life, even in my early teens.

Does anyone know if there are good books, particularly on combinatorics, aimed at people in middle or high school? I'm thinking particularly of one enthusiastic young programmer of my acquaintance.

(Note: I have moved this question from its original posting on StackOverflow. Before it was removed from there, someone suggested Concrete Mathematics and Bryant's Aspects of Combinatorics, both of which are even harder than the various books by Grimaldi, Epps, Rosen, and Roberts, which I used in college-level courses. Someone else suggested Martin Gardner's books. But actually, I'm looking for something more systematic than math games yet aimed at a less mature reader than a college-level textbook.)

How about Ross Honsberger's Mathematical Gems and Mathematical Morsels? The math in those books should be accessible to a motivated middle school student. These books have a pretty diverse collection of topics and there is a lot of discrete math in them, so they seem to satisfy your conditions.

I was a middleschool student when I read the Morsels. It was really challenging for me, and almost impossible for my peers. But despite that, I recommend that book.
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picakhuApr 7 '11 at 23:50

Thanks. This looks good. The sole Amazon reader review of Mathematical Gems III says, "For Martin Gardner fans in search of something a little more highly engineered, Gems II and III will prove to be a sound investment." I'll be glad to hear other suggestions, too, though.
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brannerchineseApr 8 '11 at 0:06

For the record, the book in question is here. Honsberger is the author of a whole series of Mathematical Plums, Mathematical Delights, Mathematical Chestnuts, Mathematical Diamonds, etc. etc.
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brannerchineseApr 8 '11 at 0:14

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@texmad - I should have mentioned that Honsberger had many more similarly themed books. Your middle school student would have enough to keep him occupied to high school and beyond.
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svenkatrApr 8 '11 at 2:48

You might look into the Art of Problem Solving books; these are specifically for younger people since they're for people who want to compete in middle and high school competitions. I haven't read them, though.

I was going to suggest these as well. The series is specifically designed for better math students in grades 6-12 and goes from algebra to calculus but includes 3 or 4 books on discrete math that most students wouldn't see. They teach everything a student needs to know, i.e., you learn the same stuff you would if you were just taking some class in high school. But, there is also the emphasis on problem solving.
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GraphthApr 8 '11 at 2:09

That sounds very good. In high school, I always felt there was a tactical aspect to problem solving that I was too impatient to look for, and as I got older I got better at finding them. I'd like to think that young people are getting actual training in how to attack problems methodically.
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brannerchineseApr 8 '11 at 2:59

I'm rather in shock over the price, though. I guess this is officially a 'textbook'. There's a paperback version listed, but it turns out to be merely the student solutions manual.
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brannerchineseApr 24 '11 at 10:23